What is the result of rotating a point (5, 0) by 180° about the origin?

Rotating the point (5, 0) by 180° about the origin results in the point (-5, 0).

When you rotate a point by 180° about the origin, you essentially flip it to the opposite side of the coordinate plane. This means that both the x-coordinate and the y-coordinate of the point will change signs. For the point (5, 0), the x-coordinate is 5 and the y-coordinate is 0. After a 180° rotation, the x-coordinate becomes -5 and the y-coordinate remains 0. Therefore, the new coordinates of the point are (-5, 0).

To understand this better, imagine the point (5, 0) on a graph. It is 5 units to the right of the origin. When you rotate it 180°, it moves to the opposite side of the origin, which is 5 units to the left. This is why the x-coordinate changes from 5 to -5. The y-coordinate does not change because the point is already on the x-axis, so it remains 0.

This concept is part of coordinate geometry, where transformations like rotations, reflections, and translations are used to move points and shapes around the plane. Rotating by 180° is a straightforward transformation because it simply involves changing the signs of both coordinates. This rule applies to any point, not just (5, 0). For example, rotating the point (a, b) by 180° would result in the point (-a, -b).